Date: Mar 24, 2013 6:19 AM
Author: William Hughes
Subject: Re: Matheology § 224

On Mar 24, 11:04 am, WM <mueck...@rz.fh-augsburg.de> wrote:


Your proof covers all lines. We have for all lines l
of the list.

if l and all its predecessors are removed
and no other line is removed,
then the union of all lines is not changed"




However, there is no information about what will
happen if you try to apply this to two
lines e.g. l along with all its predecessors
and m along with all its predecessors.

Now it is easy to see what will happen in this
case. Since we can replace l and m with
one of either l or m, we know what will happen
if we remove two lines.

Since we can replace l,m and p with
one of either l or m or p, we know what will happen
if we remove three lines.

It is easy to see we know what
will happen if we remove a natural
number of finite lines.

However, we do not know what will happen
if we remove an infinite number of
finite lines.